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How shall we say "不甘心“ in English? For example, "经历多次失败后，仍然不甘心放弃过去的种种努力和自己的理想”.

Note that "is not willing to" means "不愿意“， still not exactly "不甘心“. Consider an example, "经历多次失败后，仍然不甘心放弃自己的理想”， “不愿意帮助他”。 In the first example, “不愿意“ doesn't have the exact meaning of "不甘心“, while in the second example, “不愿意“ cannot be replaced with "不甘心“.